Received Capita Home Office Enforcement letter

In June 2013 my Fiancee from the Philippines, the mother of our now 3 yr old, was refused flr as an overstayer with no appeal, not removed. I am British born n bred. She has recently received a letter from Capita stating the Home Office intends to commence removal proceedings and she must complete the form stating her intentions for departure.

Accepting that once her case was decided back in June 2013 our then legal aid solicitors did not want to know and gave us no helpful advice going forward. Clearly we do not want her to just tick the box and leave - how is that right or fair on our British 3 year old son who is thriving THANKS to HER?!!!
She has overstayed since 2004. There is a tick box on the Capita letter for the statement if she does not intend to leave (advises seeking legal advice which I guess we'll have to, though I can ill afford this as of course she does not work, so have been in a cruel catch 22)

She was refused on the basis we had not lived together at that point for 2 years; our son was only a few months old in June 2013. We have lived together since Sept 2012. Additionally as she did not have sole parental responsibility.

Not really sure what my question is; is removal likely? would this generate an appeal, potentially winnable? Cost? How quickly generally are they likely to commence removal action, weeks, months?

I know the general advice will be to seek legal advice; hoping for something to keep me going until then...

Thanks

D

Maybe look at submitting an FLR(FP) 10 year partner route application.